HAL Id: hal-00767727https://hal.archives-ouvertes.fr/hal-00767727v1

Submitted on 20 Dec 2012 (v1), last revised 7 Jan 2013 (v2)

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

New Physics-Based Turbocharger Data-MapsExtrapolation Algorithms: Validation on a

Spark-Ignited EngineJamil El Hadef, Guillaume Colin, Vincent Talon, Yann Chamaillard

To cite this version:Jamil El Hadef, Guillaume Colin, Vincent Talon, Yann Chamaillard. New Physics-Based TurbochargerData-Maps Extrapolation Algorithms: Validation on a Spark-Ignited Engine. 2012 IFAC Workshopon Engine and Powertrain Control, Simulation and Modeling (ECOSM), Oct 2012, Rueil-Malmaison,France. �hal-00767727v1�

https://hal.archives-ouvertes.fr/hal-00767727v1https://hal.archives-ouvertes.fr

New Physics-Based Turbocharger Data-Maps Extrapolation Algorithms:

Validation on a Spark-Ignited Engine

J. El Hadef *, G. Colin*, V.Talon**, Y.Chamaillard*

*Laboratoire PRISME, 8 rue Léonard de Vinci, 45000 Orléans cédex 2, FRANCE (Tel: +33238494383; e-mail: jamil.el-

hadef@etu.univ-orleans.fr).

** Renault SA - CTL, 1 Allée de Cornuel, 91510 Lardy, FRANCE (Tel: +33611527597; e-mail: vincent.talon@renault.com)

Abstract: Objectives in terms of pollutant emissions and fuel consumption reduction, as well as

development costs and time to market reduction, has led car manufacturers to use more and more system

simulation. However, among all the fields in which it has enabled to achieve these goals, the control

development stage is one of those, in which major improvements can still be achieved. In this context and

with the increasing penetration of downsized engines, turbocharger modeling has become one of the

biggest challenges in engine simulation. This paper focus on the validation of compressor and turbine

data maps, extrapolated using new physics-based extrapolation algorithms. The study led to excellent

prediction performances for two classical control-oriented models. Conclusions stress: 1- The

improvement of the extrapolation robustness, in particular in the low turbocharger rotational speeds zone.

2- The possibility to keep a low calculation time as well as maintaining the same calibration effort.

Keywords: Turbocharger, data-maps, interpolation, extrapolation, validation, transients, steady-state.

1. INTRODUCTION

Always more drastic pollutant emission standards constrained

the car manufacturers to reduce the fuel consumption and

pollutant emissions of internal combustion engines. This can

be achieved by reducing the engine displacement as well as

adding a turbocharger to the air path in order to maintain the

same driving performances. In this context, model-based

development strategies are a very promising way to deal with

this increasing complication of engines technical definition

(Gissinger et al., (2002), Dauron, (2007), Guzzella et al.,

(2004)). In fact, model-based development strategies such as

validation on virtual test bench as well as model-embedded

control are now widely integrated in car manufacturers’ development processes and research programs.

In the case of turbocharged engines, the turbocharger sub-

model accuracy represents the biggest challenge. Usually, for

calculation time considerations, it relies on extrapolated

manufacturer’s data maps. The goal of this study is to confirm that new physics-based extrapolation algorithms (El

Hadef et al., (2012)) implemented in classical zero dimension

engine models (usually implemented using commercial

software or in any programming language) lead to accurate

results, without increasing the calibration effort. The results

for two different models are presented in this paper: first, a

reference simulator implemented using the commercial

software LMS AMESim, then, a Matlab code designed to be

embedded in a control law.

2. ENGINE TECHNICAL DEFINITION

The work is based on a multi-points injection 1.2L

turbocharged spark-ignited engine (see figure 1). Such a light

technical definition increases the turbocharger importance.

As a consequence, it makes possible to estimate the benefit

induced by the new data-maps in control-oriented models.

Fig. 1. Engine and sensors configuration used for the study.

The engine is a turbocharged four-cylinder spark-ignited

engine. Actuators actual position is also recorded.

Injection and throttle command and response have been

recorded. The wastegate actual position could not be

measured on the engine available for the study.

Pressure and temperature before and after each air path

component have been acquired. The engine rotational speed

and torque as well as the turbocharger rotational speed have

also been measured.

3. REFERENCE SIMULATOR

A 0D mean value model has been developed to be used as a

virtual test bench for the control development stage. Most of

the components are taken from the IFP engine library. The

Pamb qamb Pavc qavc Papc qapc Pape qape Pman qman

Pavt Tavt

Papt qapt wtNe

Air Filter

Heat

exchanger Throttle

Wastegate

Catalyst

&

Muffler

Compressor

Turbine

Inlet manifold

Outlet manifold

others are part of the mechanical and signal AMESim library,

included in the standard package.

This model has been validated in steady state conditions as

well as for transients. As such, it can be used to validate the

control law using, for example, hardware in the loop testing.

3.1 Mean value engine model

A mean value engine model component provides the air mass

flow rate, the engine torque, the friction torque and the

energy given to the exhaust. All these outputs are estimated

from data-maps which can be determined from the physical

quantities available for the study (see figure 1).

This sub-model can be pre-validated by setting inlet and

outlet manifold pressures, the inlet manifold temperature, the

air-fuel ratio and the engine speed. In those conditions, the

sub-model must already provide the right flow rate, torque

and outlet manifold temperature.

3.2 Air path calibration

The air path of the model contains component sub-models for

the air filter, the catalyst and the muffler. They are all based

on a flow restriction model. The effective cross section

parameter is calibrated to match the test bench data points.

For the throttle and the wastegate, a flow restriction model is

also used. In the first case, the effective area is known for

every position of the actuator. For the wastegate, a PID

controller determines the effective area which matches the

inlet manifold pressure.

The heat exchanger is modelled as the combination of a

standard heat exchanger and a flow restriction. The first one

is set to match the inlet manifold temperature test bench data

points. The second one is calibrated to match the pressure

drop measured on the test bench (see figure 1).

The compressor and turbine models both rely on data-maps

for pressure ratio, flow rate and efficiency. These data-maps

are extrapolated from manufacturer’s steady state data points. An innovative physical-based extrapolation strategy has been

developed and is presented in section 5 (El Hadef et al.,

(2012)).

Compressor and turbine models are mechanically linked by a

shaft which inertia is supposed to be known.

4. CONTROL EMBEDDED MODEL

A control embedded model must combine accuracy and

stability while keeping a low calculation time. In this case, a

0D approach combined with a mean value cylinders model

usually appears to be the most appropriate (Moulin et al.,

(2008)). The model described below is a four-state 0D model

which has been validated on steady state operations as well as

on transients.

4.1 Air path discretization

The strategy used here discretizes the pipes into control

volumes (see figure 2). Each of them represents a state of the

model and as such, its dynamic is governed by a differential

equation. Between each of them, an orifice (usually a flow

restriction) controls the flow rate at the inlet (respectively at

the outlet) of the control volume (see figure 2).

Fig. 2. Air path discretization: control volumes and

restrictions.

In this model, the throttle and the wastegate are treated as

flow restriction, while a data-map based model is used for the

compressor and the turbine. In order to validate it, the same

innovative data-maps construction as for the reference

simulator is used here and detailed in section 5.

4.2 Reservoir model

In each control volume, Euler’s mass, energy and momentum equations are applied: 擢陳擢痛 噺 芸陳沈津 伐 芸陳任祢禰 (1) 擢帳擢痛 噺 芸陳沈津 岾月沈津 髪 怠態懸沈津態峇 伐 芸陳任祢禰 岾月墜通痛 髪 怠態懸墜通痛態峇 (2) 擢陳塚擢痛 噺 畦岫鶏沈津 髪 貢沈津懸沈津態岻 伐 畦岫鶏墜通痛 髪 貢墜通痛懸墜通痛態岻 (3) where m is the mass, E the energy, v the flow speed, Qm the

mass flow rate, h the enthalpy, A the cross section, P the

pressure and the fluid density. Indices “in╊ and “out╊ respectively stand for inlet and outlet of the considered

control volume.

Neglecting the kinetic energy in the energy (2) and the 貢懸態 term in the momentum (3), the enthalpy flow can be deduced: 芸朕 噺 芸陳系椎肯 (4) where Qh is the enthalpy flow, Cp the specific heat at constant

pressure and 肯 the temperature. It leads to the derivative of the internal energy U: 擢腸擢痛 噺 芸陳日韮系椎日韮肯沈津 伐 芸陳任祢禰系椎任祢禰肯墜通痛 (5) where U is the internal energy.

In a given volume V, it is directly linked to the pressure

derivative: 擢牒擢痛 噺 廷貸怠蝶 擢腸擢痛 (6) where is the ratio of specific heats.

Qcomp

Pape Pape

Qthr

Heat

exchanger

+ PipesThrottleCompressor

Qthr

Pman Pman

QengInlet manifold

Qfuel Cylinders

Outlet manifold

Turbine

Wastegate

Pavt

Pavt

Qturb

Qwg

Orifice

Control volume

Under the assumption of constant temperature in the reservoir

(Hendricks, (2001)), only one state equation governs the

dynamic of the control volume. It is given in Martin et al.,

(2009b) by: 擢牒擢痛 噺 廷追蝶 盤芸陳日韮肯沈津 伐 芸陳任祢禰肯墜通痛匪 (7) where r is the fluid gas constant.

The specific heat at constant pressure must then be defined as 系椎 噺 廷追廷貸怠 (8) As described in figure 2, the model contains three control

volumes: the heat exchanger, the inlet manifold and the outlet

manifold. In each of them, the pressure dynamic is computed

using (7).

4.3 Orifice models

Inlet and outlet flow rates of control volumes are controlled

by the orifices which separate them. For the throttle and the

wastegate, a flow restriction model is used (Moulin et al.,

(2008)).

The flow is supposed to be compressible and isentropic.

Under this hypothesis, the flow can be estimated using the

pressure upstream and downstream the orifice (Heywood,

(1988), Talon, (2004)):

菌衿芹衿緊芸陳 噺 牒祢濡紐追脹祢濡 鯨勅捗捗ヂ紘 岾 態廷袋怠峇 婆甜迭鉄岫婆貼迭岻 件血 牒匂濡牒祢濡 半 岾 態廷袋怠峇 婆婆貼迭芸陳 噺 牒祢濡紐追脹祢濡 鯨勅捗捗 岾牒匂濡牒祢濡峇迭婆俵 態廷廷貸怠峭な 伐 岾牒匂濡牒祢濡峇婆貼迭婆 嶌 剣建月結堅拳件嫌結(9) where 鯨勅捗捗 is the effective area of the orifice. The indices “us╊ and “ds╊ respectively stand for upstream and downstream.

4.4 Temperatures

To establish (7), a constant temperature hypothesis has been

done. This is the result of the fact that the dynamic of the

temperature is considered to be slower than the pressure one.

One can then consider: 擢提擢痛 噺 ど (10) As a result, the temperature in each reservoir can be

computed algebraically. Many models exist in literature and

depend of the considered volume. The one chosen here will

be detailed on a case-by-case basis in the next sub-sections.

4.5 Compressor model

The compressor is considered in the model as a flow rate

source. The flow rate is read in a data-map f1 provided by the

manufacturer and extrapolated as detailed in section 5: 芸頂墜陳椎 噺 血怠盤講頂墜陳椎 ┸ 降痛匪 (11) where Qcomp is the compressor outlet mass flow rate, 講頂墜陳椎 the compression ratio and 降痛 the turbocharger rotational speed. 血怠 is the extrapolated data-map.

The flow rate is distributed at a given temperature which

depends of the compressor isentropic efficiency. It is

compute algebraically using:

肯銚椎頂 噺 肯銚陳長 蕃訂迩任尿妊婆貼迭婆 貸怠挺迩任尿妊 髪 な否 (12) where 肯銚椎頂 is the temperature downstream the compressor, 肯銚陳長 the atmospheric temperature and 考頂墜陳椎 the compressor isentropic efficiency.

The isentropic efficiency of the compressor is read in a

second data-map, also extrapolated from manufacturer’s data: 考頂墜陳椎 噺 血態盤芸頂墜陳椎 ┸ 降痛匪 (13) where 血態 is the extrapolated data-map. 4.6 Turbine model

The turbine is modelled as a flow restriction which flow rate

is directly read from a data-map: 芸痛通追長 噺 血戴岫講痛通追長 ┸ 降痛岻 (14) where Qturb is the turbine flow rate and 講痛通追長 the expansion ratio. 血戴 is an extrapolated data-map. The temperature of the flow at the outlet of the turbine can be

obtained from the turbine isentropic efficiency: 肯痛通追長 噺 肯銚塚痛 峪な 伐 考痛通追長 峭な 伐 岾 怠訂禰祢認弐峇婆貼迭婆 嶌 崋 (15) where 肯痛通追長 is the turbine outlet temperature, 肯銚塚痛 the outlet manifold temperature and 考痛通追長 the turbine isentropic efficiency.

As for the compressor, the turbine isentropic efficiency is

read in a data-map 血替: 考痛通追長 噺 血替岫講痛通追長 ┸ 降痛岻 (16) 4.7 Mechanical turbocharger model

The particularity of the compressor and the turbine, as flow

sources, is that they are mechanically linked. Neglecting

frictions, the dynamical behaviour of the turbocharger is

given by a fourth state equation which complete the model

(Chauvin et al., (2011), Moulin et al., (2008)): 降痛岌 噺 怠徴 岾劇槌禰祢認弐 伐 劇槌迩任尿妊峇 (17) where 蛍 is the turbocharger inertia, 劇槌禰祢認弐 and 劇槌迩任尿妊 respectively represent the turbine and compressor torques.

Compressor and turbines torques are computed using the

model described above. In both cases, they depend on the

mass flow rate, the inlet and outlet temperature and the

turbocharger rotational speed: 劇槌迩任尿妊 噺 町迩任尿妊抜寵妊抜盤提尼妊迩貸提尼尿弐匪摘禰 (18) 劇槌痛通追長 噺 町禰祢認弐抜寵妊抜岫提尼寧禰貸提禰祢認弐岻摘禰 (19)

4.8 Mass flow rate and volumetric efficiency

The flow rate 芸勅津直 is defined as a function of the inlet manifold pressure and temperature as well as the engine

speed (Heywood, (1988), Moulin et al., (2008)): 芸勅津直 噺 牒尿尼韮蝶迩熱如追提尿尼韮 朝賑怠態待 抜 考塚墜鎮 (20) where Qeng is the engine flow rate, Pman and 肯陳銚津 the manifold pressure and temperature, Vcyl the engine

displacement, Ne the engine rotational speed and 考塚墜鎮 the volumetric efficiency.

The strategy consists to first calculate the theoretical mass

flow rate at inlet manifold conditions, under the hypothesis of

a perfect gas. This quantity is then multiplied by the

volumetric efficiency 考塚墜鎮 which represents the ability of the engine to aspire this quantity of air from the manifold.

This ability directly depends from the geometry of the engine

and the operating points: 考塚墜鎮 噺 血泰 岾軽勅┸ 牒尿尼韮脹尿尼韮峇 (21) where 血泰 is a second order polynomial calibrated on the steady state test bench measurements (average relative error

is 1.7% with a standard deviation of 1.4% while maximum

relative error is 8.9%).

4.9 Exhaust mass flow rate

At the outlet of the cylinders, the flow rate is the sum of the

inlet mass flow rate described above and the fuel mass flow

rate. The last one, if not known, can be computed using the

air-fuel ratio AFR: 芸捗通勅鎮 噺 芸勅津直 抜 凋庁眺怠替┻胎 (22) where Qfuel is the fuel mass flow rate and AFR the air-fuel

ratio.

4.10 Exhaust enthalpy flow rate and exhaust temperature

As underlined in Eriksson, (2007), when considering

turbocharged engines, the exhaust enthalpy flow rate is

essential. In fact, it represents the potential power that can be

recovered by the turbine and as such, influences the intake air

charge.

The outlet manifold temperature is computed using the inlet

gas conditions (mass flow rate and temperature) and the fuel

mass flow rate: 肯銚塚痛 噺 肯陳銚津 髪 倦勅頂朕 町肉祢賑如抜挑張蝶寵妊盤町肉祢賑如袋町賑韮虹匪 (23) where LHV is the lower heating value and 倦勅頂朕 represents the amount of energy which is transferred to the exhaust pipes

flow. A polynomial model of second order is used to

compute this quantity for every operating point: 倦勅頂朕 噺 血滞盤軽勅 ┸ 芸捗通勅鎮 ┸ 芸勅津直匪 (24) where 血滞 is a second order polynomial which coefficients are calibrated from steady state test bench data points (average

relative error is 1.8% with a standard deviation of 1.4% while

maximum relative error is 6.3%).

4.11 Summary

The model is described by four differential equations. Three

of them concern the pressure dynamic in the control volumes

and are of the form of (7). The last one describes the

turbocharger dynamic (see (17)).

For computation time consideration, the use of a discrete

form is highly recommended to compute the variable at step

k+1 from values at step k:

菌衿衿芹衿衿緊鶏銚椎勅賃袋怠 噺 鶏銚椎勅賃 髪 廷追蝶尼妊賑 盤芸頂墜陳椎肯銚椎頂 伐 芸痛朕追肯銚椎勅匪つ建鶏陳銚津賃袋怠 噺 鶏陳銚津賃 髪 廷追蝶尿尼韮 肯陳銚津盤芸痛朕追 伐 芸勅津直匪つ建 叩旦担賃袋怠 噺 鶏銚塚痛賃 髪 廷追蝶尼寧禰 肯銚塚痛盤芸勅津直 髪 芸捗通勅鎮 伐 芸痛通追長 伐 芸栂直匪つ建ù担賃袋怠 噺 降痛賃 髪 怠徴 岾劇槌禰祢認弐 伐 劇槌迩任尿妊峇 つ建

(25)

where Vape, Vman and Vavt respectively represent the volume between the compressor and the throttle, the volume of the

inlet manifold and the outlet manifold volume (see figure 2).

Qthr and Qwg stand for the throttle and wastegate flows, both

obtained with (9). t is the sampling time and equal to 1 ms.

5. TURBOCHARGER DATA-MAPS EXTRAPOLATION

Most turbocharger models, which can be found in literature,

are based on data-maps. However, the data-maps provided by

turbocharger manufacturers usually only contain few points

at high iso-speeds (data points are usually only provided for

iso-speeds greater than 40% of the maximum turbocharger

rotational speed). That’s why, in order to simulate realistic driving cycles, the information at lower rotational speeds

must be extrapolated.

In this context, a new physical-based strategy of extrapolation

has been developed in order to tackle the different problems

induced by current methods (Jensen et al., (1991), Martin et

al., (2009b), Moraal et al., (1999)). These algorithms are fully

detailed and proven in El Hadef et al., (2012).

5.1 Compressor pressure ratio

For the compressor mass flow rate (see figure 3), an analysis

of the general turbo machinery equations (see El Hadef et al.,

(2012)) has led to a new physics-based algorithm. It relies on

the dimensionless head parameters 皇 and flow rate 溝 (Martin et al., (2009a)): 皇 噺 凋岫摘禰岻袋喋岫摘禰岻貞寵岫摘禰岻貸貞 (26) where the head parameter 皇 and the dimensionless flow rate 溝 are respectively a normalisation of the pressure ratio 講頂墜陳椎 and the mass flow rate 芸頂墜陳椎 and A, B and C are fitted using gradient optimization algorithm on manufacturer’s data points.

Using monotone piecewise cubic interpolation has

demonstrated very accurate results in this case (Draper et al.,

(1998), Fritsch et al., (1980)).

Fig. 3. Compression ratio 講頂墜陳椎 versus reduced mass flow rate QcompRED. For each supplier’s iso-speed, the pressure ratio is plotted (solid lines) and compared to the manufacturer’s points (white stars). New iso-speeds, interpolated and

extrapolated, are also presented (dash-dot lines).

Another advantage of the model presented here is that (26)

can directly be inverted to compute the exact inverted data

map which is required in (11). In fact, one can easily write: 溝 噺 大岫摘禰岻堤貸代岫摘禰岻台岫摘禰岻袋堤 (27) 5.2 Compressor isentropic efficiency

The isentropic efficiency of the compressor 考頂墜陳椎 (see figure 4) is given by the ratio of the isentropic specific enthalpy

exchange ッ月沈鎚 and the specific enthalpy exchange ッ月: 考頂墜陳椎 噺 綻朕日濡綻朕 (28) When the head parameter has been extrapolated with (26),

the isentropic specific enthalpy exchange can be directly

deduced through the entire operating range: ッ月沈鎚 噺 怠態皇戟頂態 (29) where Uc is the blade tip speed :

戟頂 噺 訂滞待経頂降痛 (30) where Dc is the wheel diameter.

One can notice that the improvements achieved on the

extrapolation of the expansion ratio have a direct influence

here.

For the specific enthalpy exchange, Martin has proven that it

is described by a linear equation (Martin et al., (2009a),

Martin et al., (2009b)), particularly adapted to be fitted: ッ月 噺 決岫降痛岻 伐 欠岫降痛岻芸頂墜陳椎眺帳帖 (31) where, a and b are second order polynomials fitted using gradient optimization algorithm on the manufacturer’s data points and 芸頂墜陳椎眺帳帖 is the reduced compressor flow rate (Eriksson, (2007), Eriksson et al., (2002)).

Fig. 4. Isentropic efficiency comp versus reduced mass flow rate QcompRED. The extrapolated compressor efficiency (solid

lines) well suits to the manufacturer’s data points (white and black stars) through the entire flow rate range. New iso-

speeds, interpolated and extrapolated, are also presented

(dash-dot lines).

5.3 Turbine pressure ratio

In literature, the turbine is usually modelled as a flow

restriction. Its flow rate (see figure 5) is given by the

standard equations of compressible gas flow through an

orifice (Moulin et al., (2008)): 芸痛通追長眺帳帖 噺 鯨 抜 撃津鎚 (32) where 芸痛通追長眺帳帖 is the reduced turbine mass flow rate (Eriksson, (2007), Eriksson et al., (2002)), 鯨 the equivalent section and 撃津鎚 the reduced flow speed which depends of the flow state (subsonic or supersonic, see (9)).

Fig. 5. Extrapolated reduced flow rate QturbRED versus

pressure ratio 講痛通追長. For each manufacturer’s iso-speed, the turbine flow rate extrapolated through the whole pressure

ratio operating range is presented (solid line) as well as the

reference points that have been used to fit the model (black

and white stars). New iso-speeds, interpolated and

extrapolated, are also presented (dash-dot lines).

The performance of such a model essentially relies on the

definition that is given to the equivalent section 鯨.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.081

1.5

2

2.5

3

3.5

QcompRED

co

mp

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

QcompRED

co

mp

1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

turb

Qtu

rbR

ED

Definitions used in literature (Jensen et al., (1991), Martin et

al., (2009b), Moraal et al., (1999)) usually show good

performance locally (i.e. around the manufacturer’s data points). However, they also suggest that the flow rate tend to

infinite at high pressure ratio. This is not what is observed

experimentally. In fact, from experimental observations, one

can define three hypotheses for the evolution of the

equivalent section with respect to the reduced mass flow rate

defined in (32):

H1: 鯨 is strictly monotonic with 講痛通追長 H2: 健件兼牒日禰蝦怠 鯨 噺 ど H3: 健件兼牒日禰蝦袋著 鯨 噺 潔剣券嫌建欠券建 According to these hypotheses, a completely new definition

of 鯨 has been proposed: 鯨 噺 倦怠 抜 蕃な 伐 結磐怠貸 迭肺禰祢認弐卑入鉄岫狽禰岻否 (33)

where k1 is a constant and k2 a second order polynomial.

Both are fitted using gradient optimization algorithm on the

data provided by the manufacturer.

5.4 Turbine isentropic efficiency

The isentropic efficiency (see figure 6) is calculated in the

same manner as for the compressor: 考痛通追長 噺 綻朕綻朕日濡 (34) Under the hypothesis of constant fluid density (Vitek et al.,

(2006)), the specific enthalpy exchange is calculated using a

linear equation (Martin et al., (2009a), Martin et al., (2009b)): つ月 噺 潔岫降痛岻芸痛通追長眺帳帖 髪 穴岫降痛岻 (35) where c and d are second order polynomials calibrated from manufacturer’s data points using regression analysis.

The isentropic specific enthalpy exchange only depends on

the pressure ratio. It is computed with: つ月沈鎚 噺 峭な 伐 岾 怠訂禰祢認弐峇婆貼迭婆 嶌 系椎劇銚塚痛 (36)

Fig. 6. Extrapolated isentropic efficiency turb. The turbine isentropic efficiency is extrapolated through the entire

expansion ratio range 講痛通追長 (solid lines) and compared to the reference values provided in the initial data-map (white and

black stars). For these iso-speeds the model well fits to the

supplier’s points. New iso-speeds, interpolated and extrapolated, are also presented (dash-dot lines).

6. RESULTS AND DISCUSSION

6.1 Steady-state reference simulator performances

As it is detailed in section 3, the building of the model is only

based on steady state test bench operating points. The model

performances for these steady state points are illustrated in

figures 7 to 9.

Fig. 7. Steady-states pressures validation for the reference

simulator. For each physical quantity, correlation lines are

plotted on the left. A perfect model would give 45 degrees

tilted straight line. Dashed lines show variation zones

specified in the title. Relative error versus test bench

measurement is plotted on the right.

Fig. 8. Steady-states turbocharger rotational speed validation

for the reference simulator.

1 1.5 2 2.5 3 3.5 4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

turb

turb

1.1 1.2 1.3 1.4 1.5 1.6 1.7

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Measurements

LM

S A

ME

Sim

Estim

atio

n

Compressor outlet pressure [bar] | +/-5%

1 1.2 1.4 1.6 1.80

1

2

3

4

5

6

7

Compressor outlet pressure [bar]

Re

lative

err

or

[%]

0.4 0.6 0.8 1 1.2 1.4 1.6

0.4

0.6

0.8

1

1.2

1.4

1.6

Measurements

LM

S A

ME

Sim

Estim

atio

n

Inlet manifold pressure [bar] | +/-5%

0 0.5 1 1.5 20

5

10

15

20

25

Inlet manifold pressure [bar]

Re

lative

err

or

[%]

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Measurements

LM

S A

ME

Sim

Estim

atio

n

Outlet manifold pressure [bar] | +/-5%

1 1.5 2 2.5 30

5

10

15

20

25

Outlet manifold pressure [bar]

Re

lative

err

or

[%]

0.5 1 1.5 2

x 105

0.5

1

1.5

2

x 105

Measurements

LM

S A

ME

Sim

Estim

atio

n

Turbocharger RPM | +/-5,000

0 0.5 1 1.5 2

x 105

0

0.5

1

1.5

2

2.5

3

3.5x 10

4

Turbocharger RPM

Ab

so

lute

err

or

[rp

m]

Fig. 9. Steady-states temperatures validation for the reference

simulator.

6.2 Steady-state control embedded model performances

The control embedded model validation stage uses the same

steady state operating points as for the reference simulator.

All the results are presented in figures 10 to 12.

Fig. 10. Steady-states pressures validation for the control

embedded model.

Fig. 11. Steady-states temperatures validation for the control

embedded model.

Fig. 12. Steady-states turbocharger rotational speed

validation for the control embedded model.

6.3 Discussion

Both models basically have the same static behaviour. On

figures 7 to 9 and on figures 10 to 12, one can see that both

models present a low relative error (particularly at high

loads). For pressures and temperatures, the average relative

error for the AMESim model is about 10%. The average

relative error on these values for the control embedded model

is even lower. The estimation of the turbocharger speed is

less accurate. The error can reach 30,000 rpm for the

reference simulator while it reaches only 25,000 rpm for the

second model at low speeds.

For control purposes, it is crucial to capture the dynamic of

control variables, i.e. the pressures in the control volumes.

For both models, these dynamics are well estimated (see

figure 13). The relative error is less than 5% for compressor

outlet and inlet manifold pressures. The performance is a bit

higher for the outlet manifold pressure: the error can locally

reach 20% on the transient presented here, but the dynamic is

usually good. In both models, the turbocharger rotational

speed dynamic is well captured (the average error is less than

9,000 rpm), in particular at low rotational speeds and pressure

ratios, where the data are fully extrapolated.

300 320 340 360 380

300

320

340

360

380

Measurements

LM

S A

ME

Sim

Estim

atio

n

Compressor outlet temperature [K] | +/-5%

300 320 340 360 3800

1

2

3

4

5

6

7

Compressor outlet temperature [K]

Re

lative

err

or

[%]

300 305 310 315 320

300

305

310

315

320

Measurements

LM

S A

ME

Sim

Estim

atio

n

Inlet manifold temperature [K] | +/-5%

300 305 310 315 320 3250

1

2

3

4

Inlet manifold temperature [K]

Re

lative

err

or

[%]

600 700 800 900 1000 1100 1200

600

700

800

900

1000

1100

1200

Measurements

LM

S A

ME

Sim

Estim

atio

n

Outlet manifold temperature [K] | +/-5%

600 700 800 900 1000 1100 1200 13000

5

10

15

Outlet manifold temperature [K]

Re

lative

err

or

[%]

1.1 1.2 1.3 1.4 1.5 1.6 1.7

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Measurements

0D

mo

de

l E

stim

atio

n

Compressor outlet pressure [bar] | +/-5%

1 1.2 1.4 1.6 1.80

2

4

6

8

10

Compressor outlet pressure [bar]

Re

lative

err

or

[%]

0.4 0.6 0.8 1 1.2 1.4 1.6

0.4

0.6

0.8

1

1.2

1.4

1.6

Measurements

0D

mo

de

l E

stim

atio

n

Inlet manifold pressure [bar] | +/-5%

0 0.5 1 1.5 20

2

4

6

8

10

12

14

Inlet manifold pressure [bar]

Re

lative

err

or

[%]

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Measurements

0D

mo

de

l E

stim

atio

n

Outlet manifold pressure [bar] | +/-5%

1 1.5 2 2.5 30

5

10

15

20

Outlet manifold pressure [bar]

Re

lative

err

or

[%]

300 310 320 330 340 350 360 370

300

310

320

330

340

350

360

370

Measurements

0D

mo

de

l E

stim

atio

n

Compressor outlet temperature [K] | +/-5%

300 320 340 360 3800

1

2

3

4

5

Compressor outlet temperature [K]

Re

lative

err

or

[%]

300 305 310 315 320

300

305

310

315

320

Measurements

0D

mo

de

l E

stim

atio

n

Inlet manifold temperature [K] | +/-5%

300 305 310 315 320 3250

1

2

3

4

5

Inlet manifold temperature [K]

Re

lative

err

or

[%]

800 900 1000 1100 1200

800

900

1000

1100

1200

Measurements

0D

mo

de

l E

stim

atio

n

Outlet manifold temperature [K] | +/-5%

700 800 900 1000 1100 1200 13000

1

2

3

4

5

6

Outlet manifold temperature [K]

Re

lative

err

or

[%]

0 5 10 15

x 104

0

5

10

15

x 104

Measurements

0D

mo

de

l E

stim

atio

n

Turbocharger RPM | +/-5,000

0 0.5 1 1.5 2

x 105

0

0.5

1

1.5

2

2.5

3

3.5x 10

4

Turbocharger RPM

Ab

so

lute

err

or

[rp

m]

Fig. 13. Transients validation of pressures and rotational

speed for the reference simulator (blue circled line) and for

the control embedded model (black dotted line). Vehicle

measurements are also plotted (thick light coloured line).

Engine speed varies from 4,000 to 6,000 rpm while throttle

and wastegate positions vary from closed to fully opened

(including sudden opening).

6.4 Limitations

One should notice that the difference between the

measurements and the simulation results is a global error

which can be addressed to three different main sources of

error: the pulse effects, the thermal effects and the

extrapolation algorithms. The first two are not explicitly

taken into account in the model. Moreover, the part that each

phenomenon has on the error cannot be evaluated with the

data presented here. That is why a comparative study

between a 0D model based on a classical extrapolation

method or based on the new one is irrelevant.

The goal of this study was to show that any classical control-

oriented model, identified using exclusively steady states test

bench measurements and based on data maps extrapolated

using the new physics-based algorithms, leads to accurate

enough results in the context of an industrial application.

7. CONCLUSION

Extrapolated turbocharger rotational speeds zone can easily

represent 50% of a classical driving cycle. This study has

been motivated by the difficulty encountered with standard

techniques to obtain accurate data in this operating range.

Thanks to an appropriate combination of physics and

mathematical fitting tools, it has been shown that the new

extrapolation strategy leads to accurate control-oriented

engine models. The advantage is that the new algorithms are

more robust than standard methods while keeping the zero

dimensional approach and a low CPU load requirement.

REFERENCES

Chauvin, J., Grondin, O., and Moulin, P. (2011). Control

Oriented Model of a Variable Geometry Turbocharger in an

Engine with Two EGR loops. Oil & Gas Science and

Technology - Rev. IFP Energies nouvelles, 66 (4), 563-571.

Dauron, A. (2007). Model-Based Powertrain control: Many

Uses, No Abuse. Oil & Gas Science and Technology - Rev.

IFP Energies nouvelles, 62 (4), 427-435.

Draper, N. R., and Smith, H. (1998). Applied Regression

Analysis. Wiley.

El Hadef, J., Colin, G., Talon, V., and Chamaillard, Y.

(2012). Physical-Based Algorithms for Interpolation and

Extrapolation of Turbocharger Data Maps. SAE

Int.J.Engines 5(2):2012, doi:10.4271/2012-01-0434

Eriksson, L. (2007). Modeling and Control of Turbocharged

SI and DI Engines. Oil & Gas Science and Technology -

Rev. IFP Energies nouvelles, 62 (4), 523-538.

Eriksson, L., Nielsen, L., Brugard, J., and Bergström, J.

(2002). Modeling of a Turbocharged SI Engine. Annual

Reviews in Control, 26, 129-137.

Fritsch, F. N., and Carlons, R. E. (1980). Monotone

Piecewise Cubic Interpolation. SIAM Journal on Numerical

Analysis, 17 (7).

Gissinger, G., and Le Fort-Piat, N. (2002). Contrôle

Commande de la Voiture. Hermès Lavoisier.

Guzzella, L., and Onder, C. H. (2004). Introduction to

Modeling and Control of Internal Combustion Engine

Systems. Springer.

Hendricks, E. (2001). Isothermal versus Adiabatic Mean

Value SI Engine Models. 3rd IFAC Workshop, Advances in

Automotive Control, 373-378.

Heywood, J. B. (1988). Internal Combustion Engines

Fundamentals. McGraw-Hill.

Jensen, J.-P., Kristensen, A. F., Sorenson, S. C., Houbak, N.,

and Hendricks, E. (1991). Mean Value Modeling of a Small

Turbocharged Diesel Engine. SAE Technical Paper,

910070.

Martin, G., Talon, V., Higelin, P., Charlet, A., and Caillol, C.

(2009a). Implementing Turbomachinery Physics into Data-

Map Based Turbocharger Models. SAE Technical Paper,

2009-01-0310.

Martin, G., Talon, V., Peuchant, T., Higelin, P., and Charlet,

A. (2009b). Physics Based Diesel Turbocharger Model for

Control Purposes. SAE Technical Paper, 2009-24-0123.

Moraal, P., and Kolmanovsky, I. (1999). Turbocharger

Modeling for Automotive Control Applications. SAE, 1999-

01-0908.

Moulin, P., Chauvin, J., and Youssef, B. (2008). Modelling

and Control of the Air System of a Turbocharged Gasoline

Engine. Proc. of the IFAC World Conference 2008.

Talon, V. (2004). Modélisation 0-1D des Moteurs à

Allumage Commandé. PhD Thesis, Université d'Orléans.

Vitek, O., Macek, J., and Polasek, M. (2006). New Approach

to Turbocharger Optimization using 1-D Simulation Tools.

SAE Technical Paper, 2006-01-0438.

t [s]

2 4 6 8 10 12

1

1.2

1.4

1.6

1.8

Time [s]

Compressor outlet pressure [bar]

2 4 6 8 10 12

0.5

1

1.5

Time [s]

Inlet manifold pressure [bar]

2 4 6 8 10 121

2

3

Time [s]

Outlet manifold pressure [bar]

2 4 6 8 10 12

0.5

1

1.5

2

x 105

Time [s]

Turbocharger RPM